Consider a third order system described by: [x (t)] [x (t)] x (t) = A x...

 

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Consider a third order system described by: [x₁ (t)] [x₁ (t)] x₂ (t) = A x₂ (t) + Bu(t) [x3 (t)] [x3 (t)] d dt x₁ (t) ) = C | x₂ (t)/ [x3 (t) where A = 1 [0 0 0 LO 1 -2] -6] 3 -3, B = 2,C= [001]. - 1³1₁ d dt (a) Find the transfer function (b) Given that one pole of the transfer function is -2, find matrices E, F, G such that the following representation is in the diagonal, Jordan, or modified canonical form of the original system (only one form applies here): B(s) Y(s) A(s) U(s)* [v₁ (t)] [v₁ (t)] |v₂(t) = E|v₂ (t) + Fu(t) V3 (t) V3 (t) [v₁ (t)] w(t) = Gv₂ (t) V3 (t) Consider a third order system described by: [x₁ (t)] [x₁ (t)] x₂ (t) = A x₂ (t) + Bu(t) [x3 (t)] [x3 (t)] d dt x₁ (t) ) = C | x₂ (t)/ [x3 (t) where A = 1 [0 0 0 LO 1 -2] -6] 3 -3, B = 2,C= [001]. - 1³1₁ d dt (a) Find the transfer function (b) Given that one pole of the transfer function is -2, find matrices E, F, G such that the following representation is in the diagonal, Jordan, or modified canonical form of the original system (only one form applies here): B(s) Y(s) A(s) U(s)* [v₁ (t)] [v₁ (t)] |v₂(t) = E|v₂ (t) + Fu(t) V3 (t) V3 (t) [v₁ (t)] w(t) = Gv₂ (t) V3 (t)

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a To find the transfer function we can use the following steps Take the Laplace transform of both si... View the full answer